1. EEC-484/584 Computer Networks
Lecture 12
Wenbing Zhao
Cleveland State University
12/2/2018

2. Outline Quiz#3 Result New grading policy Project Data Link layer
Error Detection and Correction
DLL
Data Link
Medium Access Control (MAC)
We Cover
This SubLayer in this lecture
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EEC-484/584: Computer Networks

3. EEC-484/584: Computer Networks
EEC484 Quiz#3 Result
Average: 65, high: 80, low: 44
Q1-26.7, Q2-9.7, Q3-13, Q4-8.5, Q5-7.2
12/2/2018
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

4. EEC-484/584: Computer Networks
EEC584 Quiz#3 Result
Average: 82.2, high: 96, low: 66
Q1-36.6, Q2-12.9, Q3-14.9, Q4-9.6, Q5-8.1
12/2/2018
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EEC-484/584: Computer Networks

5. New Grading Policy
Considering the lower average scores on the first three quizzes, I decided to grade on a curve in the following way:
If the average is below 80, then your new score = your current score + (80 – average)
Else, no adjustment is done
This is done on a per quiz basis
EEC484 and EEC584 are curved separately
12/2/2018

6. EEC484 Project Walk-through
See demo
12/2/2018

7. EEC584 Project Walk-through
Searching for literature: ACM digital library and Google scholar
Example wiki pages
Example peer review
Turnitin.com account
You must submit a turnitin.com report
12/2/2018

8. Functions of Data Link Layer
Provide a virtual source-to-destination communication channel to the network layer
Dealing with transmission errors
Regulating data flow
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EEC-484/584: Computer Networks

9. Error Detection and Correction
Causes of errors
Transmission errors on phone lines due to thermal noise
Data transmission errors due to impulse noise
Signals are separated, distorted, recombined
Crosstalk between physically adjacent wires
Compression and decompression
Receiver out of synch with sender
Errors usually occur in bursts
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

10. Error-Correcting Codes
n-bit codeword – an n-bit unit containing data and check bits
m bits of data, r bits redundant/check bits (n = m+r)
How to measure the differences between two codewords (num of different bits)
Using exclusive OR and counting number of 1 bits in the result
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

11. Error-Correcting Codes
Hamming distance – number of bit positions in which two codewords differ
If two codewords are a Hamming distance d apart, it will require d single-bit errors to convert one into the other
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

12. Error-Correcting Codes
Complete code
Complete list of all legal codewords: 2m possible data messages
Recall that there are m bits of data
Hamming distance of the complete code
Find two codewords whose Hamming distance is minimum
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao 12

13. Error-Detection Codes
A distance d+1 code can detect up to d errors, why?
If there are d+1 errors, one valid codeword might be turned into another valid codeword
≤ d errors will change a valid codeword into an illegal codeword  can be detected!
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

14. Error-Correcting Codes
To correct d errors, need a distance 2d+1 code
Legal codewords are so far part that even with d changes, original codeword is still closer than any other codeword, so it can be uniquely determined
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

15. Error-Correcting Codes: Example
Consider a code with only four valid codewords
, , ,
This code has a distance 5  can correct double errors
If arrives, receiver knows the original must have been
However, if triple error changes to , the error will not be corrected properly
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

16. EEC-484/584: Computer Networks
Parity Bit
Parity bit – a single bit is appended to the data
Parity bit is chosen so that number of 1 bits in the codeword is even or odd
Example: Given
With even parity 
With odd parity 
A code with a single parity bit has a distance 2
Since any single-bit error produces a codeword with wrong parity  can be used to detect single bit errors
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

17. Error-Detecting Codes
If a single parity bit is appended to a block, error detecting probability is only 0.5 if burst error occurs (why?)
This can be improved by treating a block as a matrix, n bits wide and k bits high,
A parity bit is computed for each column and affixed to the matrix as the last row
The matrix is transmitted one row at a time
Probability of accepting bad block is 2-n
If a burst error occurs, it is equally likely to have single-bit error, double-bit error, etc.
If odd number of bits error => can detect error
If eve number of bits error => cannot detect error
Therefore, the probability of detecting error is 50%
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EEC-484/584: Computer Networks
Wenbing Zhao 17

18. Error-Detecting Codes: CRC
Polynomial code, also known as CRC (Cyclic Redundant Code)
Treat bit string as polynomial with 0 and 1 coefficients
m-bit frame: M(x) = bm-1xm-1 + … + b0
E.g.: => M(x) = x7 + x6 + x4 + x3 + x1
Use modulo 2 arithmetic
No carries or borrows: XOR
The degree of a polynomial is the maximum of the degrees of all terms in the polynomial
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

19. EEC-484/584: Computer Networks
Cyclic Redundant Code
Sender and receiver agree on generator polynomial G(x) (High & low order bits must be 1)
For a frame with m bits corresponding to M(x), m > deg G(x) = r
Append checksum to end of frame so polynomial T(x) corresponding to checksummed frame is divisible by G(x)
When receiver gets checksummed frame, divides T(x) by G(x)
If remainder R(x) != 0, then transmission error
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

20. Algorithm to Compute CRC Checksum
Let m = deg M(x), r = deg G(x)
Append r 0 bits to lower-order end of frame: xrM(x)
Divide bit string corresponding to xrM(x) by bit string corresponding to G(x)
Subtract remainder R(x) from bit string corresponding to xrM(x), result is checksummed frame. Let T(x) be its polynomial
xrM(x) = Q(x)G(x) + R(x)
xrM(x) – R(x) = Q(x)G(x) = T(x)
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

21. EEC-484/584: Computer Networks
Compute CRC Checksum
XOR
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

22. International Standard Polynomials
CRC-12 G(x) = x12 + x11 + x3 + x2 + x1 + 1
Used for 6-bit characters
CRC-16 G(x) = x16 + x15 + x2 + 1 CRC-CCITT G(x) = x16 + x12 + x5 + 1
Used for 8-bit characters
CRC-32 G(x) = x32 + x26 + x23 + x22 + x16 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x1 + 1
Used in IEEE 802
Detects all bursts of length 32 or less and all bursts affecting an odd number of bits
No need to remember these generator polynomials
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EEC-484/584: Computer Networks
Wenbing Zhao 22

23. EEC-484/584: Computer Networks
Exercise
Q1. To provide more reliability than a single parity bit can give, an error-detecting coding scheme uses one parity bit for checking all the odd-numbered bits and a second parity bit for all the even-numbered bits. What is the Hamming distance of this code?
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao

24. EEC-484/584: Computer Networks
Exercise
Q2. A bit stream is to be transmitted using the standard CRC method described in the text. The generator polynomial is x Show the actual bit string transmitted. Suppose the third bit from the left is inverted during transmission. Show that this error is detected at the receiver's end.
12/2/2018
EEC-484/584: Computer Networks
Wenbing Zhao